Method and device for determining blood volume during an extracorporeal blood treatment

ABSTRACT

The invention relates to a method for determining blood volume during extracorporeal blood circulation, which is based on measuring the propagation rate or propagation time of the pulse waves propagating in the extracorporeal circulation system. The invention preferably involves the measurement of the propagation rate or propagation time of the pulse waves generated by the blood pump, which is placed in arterial branch of the blood line. The device for determining blood volume can make use of the pressure sensor, which is placed in the venous branch of the blood line and which is already provided in prior art blood treatment devices. As a result, the amount of equipment required is relatively low.

FIELD OF THE INVENTION

The invention relates to a method for the determination of the bloodvolume during an extracorporeal blood treatment with a blood treatmentapparatus in an extracorporeal blood circuit as well as a device for thedetermination of the blood volume during an extracorporeal bloodtreatment.

BACKGROUND OF THE INVENTION

For the purpose of removing substances usually eliminated with urine andfor the purpose of withdrawing fluid, use is made of various methods formachine-aided blood cleaning or blood treatment in acute or chronickidney failure. Diffusive substance transport predominates in the caseof haemodialysis (HD), whilst convective substance transport via themembrane takes place in the case of haemofiltration (HF).Haemodiafiltration (HDF) is a combination of the two methods.

During extracorporeal blood treatment, the patient's blood flows via anarterial branch of a tube-line system into a blood treatment apparatus,for example a haemodialyser or haemofilter, and flows from the bloodtreatment apparatus via a venous branch of the line system back to thepatient. The blood is conveyed by means of a blood pump, in particular aroller pump, which is arranged in the arterial branch of the linesystem. Fluid can be withdrawn from the patient during theextracorporeal treatment (ultrafiltration).

One of the main complications with extracorporeal blood treatment is anacute drop in blood pressure (hypotony), which can be caused by anexcessively high or rapid fluid withdrawal. There are various solutionsto this problem. On the one hand, blood pressure monitors are knownwhich continuously monitor a change in the blood pressure and regulatethe ultrafiltration in dependence on the change in blood pressure. Onthe other hand, blood volume monitors are known which measure therelative blood volume during the dialysis treatment and carry out aregulation of the ultrafiltration in dependence on the relative bloodvolume.

DE-C-197 46 377 describes a device for measuring blood pressure, whichis based on the detection of the propagation rate or transit time of thepulse waves being propagated via the arterial vessel system of thepatient, said pulse waves being generated by the patient's heartcontractions.

There is known from DE-A-40 24 434 a device for the regulation ofultrafiltration, in which the pressure in the extracorporeal circuit ismonitored in order to determine the relative blood volume. The change inthe blood volume is deduced from the change in the pressure in thecourse of the blood treatment compared with the pressure at the start ofthe treatment.

There is known from DE 100 51 943 A1 a method for the non-invasive bloodpressure measurement of patients on the basis of pulse-wave transittimes during an extracorporeal blood treatment.

SUMMARY OF THE INVENTION

An object of the invention is to provide a method which permits thedetermination of the blood volume during an extracorporeal bloodtreatment without major expenditure on equipment. A further object ofthe invention is to provide a device which enables the determination ofthe blood volume during an extracorporeal blood treatment without majorexpenditure on equipment.

The method according to the invention and the device according to theinvention are based on the generation of pulse waves in theextracorporeal blood circuit, whereby the propagation rate or transittime of the pulse waves being propagated in the extracorporeal circuitis measured. The blood volume is determined from the measuredpropagation rate or transit time of the pulse waves.

The blood volume can be determined from the propagation rate or transittime of the pulse waves, because certain blood constituents, e.g.haemoglobin, proteins etc., remain in the extracorporeal blood circuit,but the plasma water is removed. Changes in the concentration of theblood constituents can thus be used to measure the change in the bloodvolume.

When mention is made of blood volume in the following, this isunderstood to mean both the absolute as well as the relative bloodvolume. The relative blood volume at time t is defined by:

$\begin{matrix}{{{RBV}(t)} = \frac{V(t)}{V(0)}} & (1)\end{matrix}$whereby

-   -   V(0) is the blood volume at time t=0, i.e. at the start of the        dialysis treatment, and    -   V(t) is the blood volume at time t, i.e. in the course of        treatment.

Since the method according to the invention and the device according tothe invention make use of the pressure measurement that is anyhowpresent in the known dialysis machines, the outlay on equipment isrelatively small. A suitable expansion of the software for themicroprocessor control of the machine is solely required for thedetermination of the blood volume.

In a preferred embodiment of the invention, the propagation rate ortransit time of the pressure pulse-waves is measured in theextracorporeal circuit, said pressure pulse-waves being caused by theblood pump which is arranged in the extracorporeal circuit of the knownhaemodialysis machines. The blood pump of the known dialysis machines isgenerally a roller pump, which generates pressure pulses with eachrotation of the pump rotor.

The pulse waves generated by the blood pump are preferably detected by apressure sensor, which is arranged in the extracorporeal circuit withknown dialysis machines.

In order to increase the accuracy, the pressure measurement can becarried out to advantage with a pressure sensor which is arrangedwithout an air column in direct contact on the blood tube or on apressure-measuring chamber provided before the latter, through which theblood line runs.

In a particularly preferred embodiment of the invention, the blood pumpis arranged in the arterial branch of the blood line upstream of theblood treatment apparatus and the pressure sensor for detecting thepulse waves downstream of the blood treatment apparatus in the venousbranch of the blood line. The section over which the transit time is tobe measured is thus the part of the blood line lying between blood pumpand pressure sensor.

If the time at which the pulse waves are generated by the blood pump isnot known, the pulse waves generated by the blood pump can be detectedwith a second pressure sensor which is arranged upstream of the bloodtreatment apparatus in the arterial branch of the blood line. The timecan however also be derived from the position of the pump rotor, whichis detected for example by a Hall sensor. The Hall sensor can have amagnet rotating with the rotor, the magnetic field whereof periodicallypenetrates a Hall probe located on the stator, a suitable electricalvoltage signal being able to be picked up at said Hall probe.

A further embodiment of the invention provides for the determination ofthe relative blood volume from the ratio of the propagation rates ortransit times of the pulse waves at two different times in the bloodtreatment, in particular at the start and during the course of thetreatment.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a very simplified diagrammatic representation of the essentialcomponents of a dialysis machine with a device for determining therelative blood volume.

FIG. 2 shows the temporal course of the signals of an arterial andvenous pressure sensor for determining the pressure in the arterial andvenous branch of the blood line and the signal of a Hall sensor fordetermining the position of the pump rotor.

DETAILED DESCRIPTION

An exemplary embodiment of a dialysis machine with a device fordetermining the relative blood volume is explained in greater detailbelow with the aid of the drawings.

The haemodialysis apparatus has a dialyser 1, which is divided by asemipermeable membrane 2 into a blood chamber 3 and a dialysing fluidchamber 4. The inlet of the blood chamber is connected to one end of anarterial blood feed line 5, into which an arterial blood pump 6 isincorporated, whilst the outlet of blood chamber 3 is connected to oneend of venous blood discharge line 7, into which a drip chamber 8 isincorporated. Blood feed line and blood discharge line 5, 7 areconventional tube lines, which form the arterial and venous branchrespectively of extracorporeal circuit I.

Blood pump 6 is a conventional roller pump, which with each rotationgenerates two pressure pulses which are propagated via blood feed line5, blood chamber 3 and blood discharge line 7 in extracorporeal bloodcircuit I. The pressure waves are generated whenever the rotor of rollerpump 6 occupies a certain position. In order to monitor the position ofthe pump rotor, roller pump 6 has a Hall sensor 33. Dialysing fluidsystem II of the haemodialysis machine comprises a device 12 forpreparing the dialysing fluid, which is connected by a first section 13of a dialysing fluid feed line to the inlet of first chamber half 14 aof a balancing device 15. Second section 16 of the dialysing fluid feedline connects the outlet of first balancing chamber half 14 a to theinlet of dialysing fluid chamber 4. The outlet of dialysing fluidchamber 4 is connected via first section 17 a of a dialysing fluiddischarge line to the inlet of second balancing chamber half 14 b. Adialysing fluid pump 18 is incorporated into first section 17 a of thedialysing fluid discharge line. The outlet of second balancing chamberhalf 14 b is connected via second section 17 b of the dialysing fluiddischarge line to a discharge 19. An ultra-filtrate line 20, which alsoleads to discharge 19, branches off from dialysing fluid discharge line17 a upstream of dialysing fluid pump 18. An ultrafiltration pump 21 isincorporated into ultra-filtrate line 20.

A second balancing chamber usually present, which is operated inparallel and phrase-shifted with respect to the first balancing chamberin order to guarantee a virtually constant flow, is not shown in FIG. 1for the sake of simplicity.

The haemodialysis machine further comprises a central control unit 22,which is connected via control lines 23 to 25 to blood pump 6, dialysingfluid pump 18 and ultrafiltration pump 21.

During the haemodialysis treatment, the patient's blood flows throughthe blood chamber and the dialysing fluid flows through the dialysingfluid chamber of the dialyser. Since balancing device 15 is incorporatedinto the dialysing fluid path, only as much dialysing fluid can flow invia dialysing fluid feed line as dialysing fluid can flow away viadialysing fluid discharge line. Fluid can be withdrawn from the patientwith ultrafiltration pump 21.

The haemodialysis machine also has a device for the non-invasivedetermination of the relative blood volume during the dialysistreatment. This device makes use of various components of thehaemodialysis machine. It is therefore part of the dialysis machine. Thedevice for determining the relative blood volume will be described indetail below.

The device for determining the relative blood volume has a pressuresensor 26 for measuring the pressure in blood feed line 5 downstream ofblood pump 6 and upstream of blood chamber 3 of dialyser 1 and apressure sensor 27 for measuring the pressure in blood discharge line 7downstream of blood chamber 3 of the dialyser. Both pressure sensors 26,27 are connected via signal lines 28, 29 to an analysing unit 30, inwhich the signals of the sensors are processed. This analysing unit is acomponent of the microprocessor control of the haemodialysis machine.From the measured pressure values, the analysing unit determines therelative blood volume, which is displayed on a display unit 31 which isconnected via a data line 32 to the analysing unit.

The functioning of the device for determining the relative blood volumeRBV will be described as follows. The determination of the relativeblood volume is based on the measurement of the transit time of thepulse waves generated by blood pump 6 which are propagated inextracorporeal blood circuit I. Measurement section L consists of theparts of the blood line and the blood chamber between arterial andvenous pressure sensors 26, 27. This section L is indicated in FIG. 1 bya′, b′ and c′.

The theoretical relationship between the pulse-wave transit time and theRBV is derived as follows. In an incompressible fluid, which is presentin an elastic cylindrical tube with cross-sectional area A, thepropagation rate c of a longitudinal pressure wave is given by:

$\begin{matrix}{c = \sqrt{\frac{Adp}{\rho\;{dA}}}} & (2)\end{matrix}$whereby

-   -   c pulse wave speed    -   ρ density of the fluid    -   dp change in pressure    -   dA change in area

During the dialysis treatment, transit time PTT (“pulse transit time”)over the part of the blood tube system (measurement section) with totallength L between the arterial pressure sensor preferably arrangeddirectly downstream of the blood pump, or more precisely the blood pump,and the venous pressure sensor amounts to:

$\begin{matrix}{{PTT} = {\frac{L}{c} = {L\sqrt{\frac{\rho}{A} \cdot \frac{dA}{dp}}}}} & (3)\end{matrix}$

From equation (3) we have:

$\begin{matrix}{{{PTT}\left( t_{0} \right)} = {L\sqrt{{\rho\left( t_{0} \right)}\left( \frac{{dA}\text{/}{A\left( t_{0} \right)}}{dp} \right)_{t_{0}}}}} & (4)\end{matrix}$

$\begin{matrix}{{{PTT}(t)} = {L\sqrt{{\rho(t)}\left( \frac{{dA}\text{/}{A(t)}}{dp} \right)_{t}}}} & (5)\end{matrix}$whereby

-   -   PTT(t₀) transit time at time t₀    -   PTT(t) transit time at time t

With equation (4) and (5), we obtain:

$\begin{matrix}{\frac{{PTT}(t)}{{PTT}\left( t_{0} \right)} = \sqrt{\frac{{\rho(t)}\left( \frac{{dA}\text{/}{A(t)}}{dp} \right)_{t}}{{\rho\left( t_{0} \right)}\left( \frac{{dA}\text{/}{A\left( t_{0} \right)}}{dp} \right)_{t_{0}}}}} & (6) \\{\left( \frac{{PTT}(t)}{{PTT}\left( t_{0} \right)} \right)^{2} = {\frac{\rho(t)}{\rho\left( t_{0} \right)}{K(P)}}} & (7) \\{{K(P)} = {\left( \frac{{dA}\text{/}{A(t)}}{dp} \right)_{t}/\left( \frac{{dA}\text{/}{A\left( t_{0} \right)}}{dp} \right)_{t_{0}}}} & (8)\end{matrix}$

Here, K(P) denotes the ratio of the expansion size of the tube at time tand t₀

The mass density of the blood is defined by the ratio of the massfraction of the protein and water in the blood to the total blood volumeby:

$\begin{matrix}{{\rho\left( t_{0} \right)} = \frac{{m_{protein}\left( t_{0} \right)} + {m_{water}\left( t_{0} \right)}}{V\left( t_{0} \right)}} & (9) \\{{\rho(t)} = \frac{{m_{protein}(t)} + {m_{water}(t)}}{V(t)}} & (10)\end{matrix}$whereby

-   ρ(t₀) mass; density of blood at time t₀-   ρ(t) mass density of blood at time t-   V(t₀) blood volume at time t₀-   V(t) blood volume at time t-   m_(protein)(t₀) mass of proteins in V (t₀) at time t₀-   m_(protein)(t) mass of proteins in V (t₀) at time t-   m_(water)(t₀) mass of water in V (t₀) at time t₀-   m_(water)(t) mass of water in V (t₀) at time t

Since the membrane of a dialyser is not permeable for the majority ofthe blood proteins, the blood protein content during haemodialysisremains approximately constant, i.e. m_(protein)(t)=m_(protein)(t₀).From equation (9), (10) and (1), we have:

$\begin{matrix}{\frac{\rho(t)}{\rho\left( t_{0} \right)} = {\frac{1}{{RBV}(t)}\left( {1 - \frac{{m_{water}\left( t_{0} \right)} - {m_{water}(t)}}{{m_{protein}\left( t_{0} \right)} + {m_{water}\left( t_{0} \right)}}} \right)}} & (11)\end{matrix}$

With m_(water)(t₀)−m_(water)(t)=V(t₀)·[1−RBV(t)]·ρ_(w), equation (11)can be written in the form

$\begin{matrix}{\frac{\rho(t)}{\rho\left( t_{0} \right)} = {\frac{1}{{RBV}(t)}\left( {1 - \frac{\rho_{w}}{\rho\left( t_{0} \right)} + {{{RBV}(t)}\frac{\rho_{w}}{\rho\left( t_{0} \right)}}} \right)}} & (12)\end{matrix}$Whereby ρ_(w) denotes the mass density of water.

With equation (7) and (12), we obtain

$\begin{matrix}{\left( \frac{{PTT}(t)}{{PTT}\left( t_{0} \right)} \right)^{2} = {\frac{1}{{RBV}(t)}\left( {1 - \frac{\rho_{w}}{\rho\left( t_{0} \right)} + {{{RBV}(t)}\frac{\rho_{w}}{\rho\left( t_{0} \right)}}} \right){K(P)}}} & (13)\end{matrix}$

The solution to this equation reads as follows:

$\begin{matrix}{{{RBV}(t)} = \frac{\left( {1 - \frac{\rho_{w}}{\rho\left( t_{0} \right)}} \right){K(P)}}{\left( \frac{{PTT}(t)}{{PTT}\left( t_{0} \right)} \right)^{2} - {\frac{\rho_{w}}{\rho\left( t_{0} \right)}{K(P)}}}} & (14)\end{matrix}$

If the tube system is elastic and remains within the proportionalityrange (elasticity range) during the treatment, K(P)=1 according toHooke's law. From this we have:

$\begin{matrix}{{{RBV}(t)} = \frac{1 - \frac{\rho_{w}}{\rho\left( t_{0} \right)}}{\left( \frac{{PTT}(t)}{{PTT}\left( t_{0} \right)} \right)^{2} - \frac{\rho_{w}}{\rho\left( t_{0} \right)}}} & (15)\end{matrix}$

Equation (15) shows that the relative blood volume RBV(t) is a functionof the ratio of the transit times and the blood density at time t₀. Onthe assumption that the blood density prior to the dialysis treatment isapproximately the same for all patients, RBV(t) depends solely on theratio of the transit times.

If, however, the elasticity of the tube depends on the pressure in thetube, in particular if there is a non-linear relationship between theelasticity and the pressure, a characteristic curve can be used forK(P).

At the start of the dialysis treatment, analysing unit 30 determinestransit time PTT(t₀) at time t₀. This value is stored in a memory. Thevalues for the mass density ρ_(w) of water and the density ρ(t₀) ofblood at the start of the dialysis treatment are also inputted into thismemory. These values are taken as constants. They can be inputtedexternally or permanently preset.

In order to determine transit time PTT(t₀), a measurement is made of thetime that a pulse wave requires in order to travel from arterialpressure sensor 26 to venous pressure sensor 27.

Even if the measurement section a′+b′+c′ in FIG. 1 permits a longmeasuring time, it needs to be taken into account that elements withdifferent elasticity are present along this section. Thus, for example,the dialyser and blood tube have different properties with respect toelasticity. In order to avoid disturbing influences, therefore,measurements can only be made over a measurement section along the bloodtube upstream or downstream of the dialyser. Either an arterial pressuresensor for measuring the transit time between the pump and the arterialpressure sensor should then be provided downstream of the blood pump ortwo venous pressure sensors should be provided for measuring the transittime between the two venous sensors.

FIG. 2 shows the temporal course of the pressure signals of pressuresensors 26, 27. It can clearly be seen that the pulse wave arrives firstat the arterial and then at the venous pressure sensor. The transit timeover measurement section L between arterial and venous pressure sensoris denoted in FIG. 2 by PTT₁. In order to have a particularly longmeasurement section, arterial pressure sensor 26 should be arrangedimmediately downstream of blood pump 6 and venous pressure sensor 27 asfar as possible downstream of blood chamber 3 in the blood line.

During the dialysis treatment, analysing unit 30 continuously determinestransit time PTT(t) of the pulse waves and continuously calculates therelative blood volume RBV(t) according to equation (15).

On the assumption of a non-linear relationship between the elasticityand the pressure, a characteristic curve for K(p) is stored in thememory. The calculation of the relative blood volume then takes placeaccording to equation (14).

An alternative embodiment of the invention provides only one venouspressure sensor 27 in blood discharge line 7. Arterial pressure sensor26 in blood feed line 5 is in principle not required. In place of thearterial pressure sensor, the occurrence of the pressure waves can bedetected with Hall sensor 33 of the blood pump.

FIG. 2 shows the Hall signal of sensor 33. It can clearly be seen thatthe negative flanks of the Hall and pressure signal coincide. Thetransit time over the section between the blood pump and the venouspressure sensor is denoted in FIG. 2 by PTT₂. Since the magnet on therotor of the blood pump leads to only one signal pre revolution and therotor has two occluding rollers, the Hall signal occurs only with halfthe frequency compared with the pressure signal.

1. A method for the determination of a blood volume during anextracorporeal blood treatment with a blood treatment apparatus in anextracorporeal blood circuit, wherein the extracorporeal blood circuitincludes an arterial branch of a blood line leading to the bloodtreatment apparatus and a venous branch of the blood line leading awayfrom the blood treatment apparatus, the method comprising: generatingpulse waves that originate in the extracorporeal blood circuit, whereinthe pulse waves have at least one of a propagation rate and a transittime; measuring the at least one of the propagation rate and the transittime of the pulse waves; and determining the blood volume from the atleast one of the measured propagation rate and the measured transit timeof the pulse waves.
 2. The method of claim 1, wherein the pulse wavesare generated by a blood pump arranged in the extracorporeal bloodcircuit.
 3. The method of claim 2, further comprising: detecting thepulse waves by a first pressure sensor arranged in the extracorporealblood circuit.
 4. The method of claim 3, wherein the blood pump isarranged in the arterial branch of the blood line upstream of the bloodtreatment apparatus, and the first pressure sensor is arranged in thevenous branch of the blood line downstream of the blood treatmentapparatus.
 5. The method of claim 4, further comprising: detecting thepulse waves by a second pressure sensor, wherein the second pressuresensor is arranged in the arterial branch of the blood line upstream ofthe blood treatment apparatus.
 6. The method of claim 1, whereindetermining the blood volume comprises determining a relative bloodvolume RBV(t) from a ratio of the at least one of the measuredpropagation rates and the measured transit times of the pulse waves attwo different times t, t₀ of the extracorporeal blood treatment.
 7. Themethod of claim 5, wherein determining the blood volume comprisesdetermining a relative blood volume RBV(t) from a ratio of the at leastone of the measured propagation rates and the measured transit times ofthe pulse waves at two different times t, t₀ of the extracorporeal bloodtreatment.
 8. The method of claim 6, wherein the relative blood volumeRBV(t) is calculated from the temporal change in the measured transittimes of the pulse waves according to the following equation:${{RBV}(t)} = \frac{1 - \frac{\rho_{w}}{\rho\left( t_{0} \right)}}{\left( \frac{{PTT}(t)}{{PTT}\left( t_{0} \right)} \right)^{2} - \frac{\rho_{w}}{\rho\left( t_{0} \right)}}$wherein PTT(t) and PTT(t₀) is the measured transit time of the pulsewaves over a segment of the extracorporeal blood circuit with apredetermined length L at time t and t₀, respectively; and wherein r_(w)is the mass density of water and r(t₀) is the mass density of the bloodat the start of the extracorporeal blood treatment.
 9. The method ofclaim 7, wherein the relative blood volume RBV(t) is calculated from thetemporal change in the measured transit times of the pulse wavesaccording to the following equation:${{RBV}(t)} = \frac{1 - \frac{\rho_{w}}{\rho\left( t_{0} \right)}}{\left( \frac{{PTT}(t)}{{PTT}\left( t_{0} \right)} \right)^{2} - \frac{\rho_{w}}{\rho\left( t_{0} \right)}}$wherein PTT(t) and PTT(t₀) is the measured transit time of the pulsewaves over a segment of the extracorporeal blood circuit with apredetermined length L at time t and t₀, respectively; and wherein r_(w)is the mass density of water and r(t₀) is the mass density of the bloodat the start of the extracorporeal blood treatment.
 10. A device for thedetermination of the blood volume during an extracorporeal bloodtreatment in an extracorporeal blood circuit, wherein the extracorporealblood circuit includes an arterial branch of a blood line leading to ablood treatment apparatus and a venous branch of the blood line leadingaway from the blood treatment apparatus, the device comprising: meansfor generating pulse waves that originate in the extracorporeal bloodcircuit, wherein the pulse waves have at least one of a propagation rateand a transit time; means for measuring the at least one of thepropagation rate and the transit time of the pulse waves; and ananalyzing unit configured to determine the blood volume from the atleast one of the measured propagation rate and the measured transit timeof the pulse waves.
 11. The device of claim 10, wherein the means forgenerating pulse waves comprises a blood pump arranged in theextracorporeal blood circuit.
 12. The device of claim 11, furthercomprising: a first pressure sensor for detecting the pulse waves,wherein the first pressure sensor is arranged in the extracorporealblood circuit.
 13. The device of claim 12, wherein the blood pump isarranged in the arterial branch of the blood line upstream of the bloodtreatment apparatus, and the first pressure sensor is arranged in thevenous branch of the blood line downstream of the blood treatmentapparatus.
 14. The device of claim 13, further comprising: a secondpressure sensor for detecting the pulse waves, wherein the secondpressure sensor is arranged in the arterial branch of the blood lineupstream of the blood treatment apparatus.
 15. The device of claim 10,wherein the analyzing unit is adapted to determine a relative bloodvolume RBV(t) from a ratio of the at least one of the measuredpropagation rates and the measured transit times of the pulse waves attwo different times t, t₀ of the extracorporeal blood treatment.
 16. Thedevice of claim 14, wherein the analyzing unit is adapted to determine arelative blood volume RBV(t) from a ratio of the at least one of themeasured propagation rates and the measured transit times of the pulsewaves at two different times t, t₀ of the extracorporeal bloodtreatment.
 17. The device of claim 15, wherein the analyzing unit isadapted to calculate the relative blood volume RBV(t) from the temporalchange in the measured transit times of the pulse waves according to thefollowing equation:${{RBV}(t)} = \frac{1 - \frac{\rho_{w}}{\rho\left( t_{0} \right)}}{\left( \frac{{PTT}(t)}{{PTT}\left( t_{0} \right)} \right)^{2} - \frac{\rho_{w}}{\rho\left( t_{0} \right)}}$wherein PTT(t) and PTT(t₀) is the measured transit time of the pulsewaves over a segment of the extracorporeal blood circuit with apredetermined length L at time t and t₀, respectively; and wherein r_(w)is the mass density of water and r(t₀) is the mass density of the bloodat the start of the extracorporeal blood treatment.
 18. The device ofclaim 16, wherein the analyzing unit is adapted to calculate therelative blood volume RBV(t) from the temporal change in the measuredtransit times of the pulse waves according to the following equation:${{RBV}(t)} = \frac{1 - \frac{\rho_{w}}{\rho\left( t_{0} \right)}}{\left( \frac{{PTT}(t)}{{PTT}\left( t_{0} \right)} \right)^{2} - \frac{\rho_{w}}{\rho\left( t_{0} \right)}}$wherein PTT(t) and PTT(t₀) is the measured transit time of the pulsewaves over a segment of the extracorporeal blood circuit with apredetermined length L at time t and t₀, respectively; and wherein r_(w)is the mass density of water and r(t₀) is the mass density of the bloodat the start of the extracorporeal blood treatment.